Hierarchical stack filtering : a bitplane-based algorithm for massively parallel processors

With the development of novel parallel architectures for image processing, the implementation of well-known image operators needs to be reformulated to take advantage of the so-called massive parallelism. In this work, we propose a general algorithm that implements a large class of nonlinear filters, called stack filters, with a 2D-array processor. The proposed method consists of decomposing an image into bitplanes with the bitwise decomposition, and then process every bitplane hierarchically. The filtered image is reconstructed by simply stacking the filtered bitplanes according to their order of significance. Owing to its hierarchical structure, our algorithm allows us to trade-off between image quality and processing time, and to significantly reduce the computation time of low-entropy images. Also, experimental tests show that the processing time of our method is substantially lower than that of classical methods when using large structuring elements. All these features are of interest to a variety of real-time applications based on morphological operations such as video segmentation and video enhancement

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Non-Additive Quantum Codes from Goethals and Preparata Codes

We extend the stabilizer formalism to a class of non-additive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of non-additive codes which are derived from Goethals and Preparata codes.Comment: submitted to the 2008 IEEE Information Theory Workshop (ITW 2008

Optimum non linear binary image restoration through linear grey-scale operations

Non-linear image processing operators give excellent results in a number of image processing tasks such as restoration and object recognition. However they are frequently excluded from use in solutions because the system designer does not wish to introduce additional hardware or algorithms and because their design can appear to be ad hoc. In practice the median filter is often used though it is rarely optimal. This paper explains how various non-linear image processing operators may be implemented on a basic linear image processing system using only convolution and thresholding operations. The paper is aimed at image processing system developers wishing to include some non-linear processing operators without introducing additional system capabilities such as extra hardware components or software toolboxes. It may also be of benefit to the interested reader wishing to learn more about non-linear operators and alternative methods of design and implementation. The non-linear tools include various components of mathematical morphology, median and weighted median operators and various order statistic filters. As well as describing novel algorithms for implementation within a linear system the paper also explains how the optimum filter parameters may be estimated for a given image processing task. This novel approach is based on the weight monotonic property and is a direct rather than iterated method